# Projectile motion in a spring loaded gun

## Homework Statement

1. A Turbo Booster toy that launches a 60-gram “insect” glider projectile by compressing a helical spring and then releasing the spring when the trigger is pulled. When pointed upward the glider should ascend approximately 8 m before falling. The launcher is made with carbon steel wire, with a diameter of d=1.1 mm. The coil diameter is D=10 mm. Calculate the number of turns N in the spring such that it would provide the necessary energy to the glider. The total working deflection is x=150 mm with a clash allowance of 10%.

## Homework Equations

I need to used conservation of energy to find initial velocity and spring constant I believe. Final velocity is 0. Not sure how to find the number of turns in the spring though.

KE=1/2*m*V^2
PE=m*g*h

## The Attempt at a Solution

g=9.81 m/s^2 gravity
d=1.1 mm wire diameter
D=10 mm col diameter
m=60 gm mass of toy
x=150 mm working deflection
dist= 8 m distance traveled

C=D/d=10/1.1= 9.091 spring index
G=11.2*10^6 psi (for carbon steel)
k=?
V=?

somehow need number of turns

Last edited:

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trying to bump this up

Redbelly98
Staff Emeritus
Homework Helper
This looks like it's outside the scope of a standard introductory physics class, which normally does not discuss how the number of turns and wire diameter related to the spring constant.

I am wondering if your professor has given you additional material on this?

At any rate, it is possible to find the spring constant k using conservation of energy methods.

minger
$$k = \frac{d^4 G}{8D^3 N}$$